In many Harry Potter university fanfictions, Neville Longbottom is a common character. He has grown into a confident and skilled wizard, and could be teaching a herbology class at the university. Draco Malfoy might also be present, either as a reformed character trying to make amends or still causing some trouble among the students. Additionally, Professor McGonagall could be in a more administrative role, overseeing the university's operations and guiding the students in a different way than she did at Hogwarts.
Hermione Granger is often a common character. She would likely be at the top of her class in the university setting, continuing her thirst for knowledge. Harry Potter himself might also be there, perhaps as a teaching assistant or a more experienced student helping others. Ron Weasley could be around too, still providing his loyalty and humor. And Luna Lovegood might be involved in some of the more unique and esoteric studies at the university.
Common characters include Ginny Weasley, who could be a star athlete in the university's Quidditch team. Fred and George Weasley might have a business set up near the university, selling their unique magical products. And Cho Chang could be a student who is involved in international magical exchange programs at the university, bringing in new ideas and cultures from other magical schools.